Torsional Response of Bridges

PaiboonPaiboon TirasitTirasitDepartment of Civil EngineeringDepartment of Civil Engineering

Tokyo Institute of TechnologyTokyo Institute of TechnologyJuneJune 1111thth , 2005, 2005

US-Japan Young Researchers Symposium on Natural NSF, US, Japan Disaster Mitigation, 2005

Inplane Rotation of Skewed Bridge Deck

F2

F1e1 e2

MT

Bridge deckColumn

Abutment

Skewed bridge(Plan view)

This probably causes seismic torsional moment coupled with other internal forces in skewed bridge piers.

Skewed bridge deck possibly rotates during an earthquake due to thecollision with the abutments or adjacent span.

Statement of ProblemsPast Experimental researches indicate that the flexural strength, stiffness and ductility of a RC member deteriorate when it is subjected to combined bending and torsional loading.

The capacities of RC piers in skewed bridges may decrease because of the existence of torsion during an earthquake.

The damage pattern of RC piers may change. The required nonlinear torsional hysteretic model for RC piers in seismic analysis of bridges has not been available.

Seismic Analysis of Skewed Bridges

Objective of Analysis

Clarify the seismic torsion response of piers in skewedbridges under the following factors

Skewed anglesPounding Steel bearing characteristicsLocking of steel bearing after failure

Representative Bridge

10 10 10

12

5.1

5.1

Transverse directionLongitudinal

direction

MB: Movable bearingFB: Fixed bearing

105

2.51.

2

2.2

Unit: meters

Finite Element ModelingElastic Deck

Transverse dir.

Longitudinal dir.

Takeda model for the moment-curvature relationship about the weak axis in the plastic hinge region Curvature

Mom

ent

GJcrack = 0.2 GJgross

Idealization of Fixed BearingsLongitudinal and transversedirections of fixed bearings

Transverse dir.

Longitudinal dir.

Fixed bearing

Transverse

Longitudinal

Transverse directionof movable bearings

Transverse dir.

Longitudinal dir.

Movable bearing

TransverseLongitudinal

Idealization of Movable Bearing

Longitudinal direction of movable bearingTransverse dir.

Longitudinal dir.

Idealization of Movable Bearing

Cable restrainer

Kcb

Transverse dir.

Longitudinal dir.

Idealization of Restrainers

50mm

Pounding Spring

kI

Transverse dir.

Longitudinal dir.

Pounding Mechanism

50mm

Time History Analysis

-10

0

10

0 10 20

Acc

eler

atio

n (m

/s2 )

Time (s)-10

0

10

0 10 20A

ccel

erat

ion

(m/s

2 )Time (s)

JMA Kobe NS Long. dir. JMA Kobe EW Transv. dir.

PGA = 8.18m/s2 PGA = 6.17m/s2

-4-2024

0 5 10 15 20Tors

ion

(MN

m)

Time (s)

2.52 MN.m

Effect of Skewed Angle

-4-2024

0 5 10 15 20Tors

ion

(MN

m)

Time (s)

-4-2024

0 5 10 15 20Tors

ion

(MN

m)

Time (s)

Pier P3Pier P1

Pier P2

40o skew No skew

3.75 MNm

1.98 MNm 2.37 MNm

1.98 MNm

P1 P2 P3-0.004-0.002

00.0020.004

0 5 10 15 20Time (s)

Inpl

ane

rota

tion

of D

eck

(rad

)

Idealization of Bearing Locking After FailureTransverse dir.

Longitudinal dir.

kI

kI

Model for additional springelement

Movement gap = 20 mm

Long. dir.RightmostBearing

Effect of Bearing Locking

-4-2024

0 5 10 15 20Tors

ion

(MN

m)

Time (s)

-4-2024

0 5 10 15 20Tors

ion

(MN

m)

Time (s)Pier P2

3.75 MNm3.71 MNm 2.37 MNm

2.52 MNm

-20

0

20

0 5 10 15 20Tors

ion

(MN

m)

Time (s)

2.52 MNm

16.8 MNm

With locking at rightmostbearing (20 mm movement gap) Without bearing locking

P1 P2 P3-0.004-0.002

00.0020.004

0 5 10 15 20Time (s)

Inpl

ane

rota

tion

of D

eck

(rad

)

Pier P3Pier P1

Combined Cyclic Bending-TorsionalLoading Test on RC Columns

Objectives

※ Clarify the stiffness, strength and ductility of RC columns under combined cyclic bending-torsionalloading.

※ Formulate an empirical model of nonlinear torsionalhysteresis of a RC column.

Columnar Specimen

Material property• Concrete : f’c = 30 MPa• Steel bar : SD295Afy = 295 MPa

eff

Japanese 1996 Design Specification for Highway Bridges

Long. reinforcement ratio = 1.27%Tie volumetric ratio = 0.79%

Experimental Setup

TOP VIEWELEVATION

Reaction frame

Vertical actuator

Horizontal actuator

Specimen

Horizontal actuators

Reaction frame

Specimen

800 mm

1350 mm

Pure Cyclic Bending under Axial Force

N

WS

E

Pure Cyclic Torsion under Axial Force

N

S

EW

Combined Bending and Torsion under Axial Force Rotation-drift ratio (θ/∆) = 2

N

WS

E

-100

-50

0

50

100

-0.1 -0.05 0 0.05 0.1To

rsio

n (k

N.m

)Rotation (rad)

Pure cyclic torsionCombined cyclic bendingand torsion (θ/∆ = 2)

-100

-50

0

50

100

-0.1 -0.05 0 0.05 0.1To

rsio

n (k

N.m

)Rotation (rad)

-150-100-50

050

100150

-80 -40 0 40 80

-4 -2 0 2 4

Late

ral f

orce

(kN

)

Displacement (mm)

Drift (%)

Pure cyclic bendingCombined cyclic bendingand torsion (θ/∆ = 2)

-150-100-50

050

100150

-80 -40 0 40 80

-4 -2 0 2 4

Late

ral f

orce

(kN

)

Displacement (mm)

Drift (%)

2.0% Drift

Comparison of Column Hystereses

24% 15%

0.01 rad

Flexural Hysteresis Torsional Hysteresis

Ultimate displacement or rotation : Displacement or rotation where the lateral force or torsion decreases to 80% of the capacity

※ Pounding between deck and abutments can result in inplane deck rotation and seismic torsion of the columns in skewed bridge during a significant earthquake.

※ Locking of bearing after damage can extensively increase the seismic torsion of piers in skewed bridges

※ The flexural capacity and the ultimate displacement of column reduce as the torsion increases. On the other hand, the increase of bending moment results in the deterioration of torsional capacity and the ultimate rotation.

※Damage of column tends to shift upward from the plastic hinge zone as the rotation-drift ratio increases.

Current Conclusions

Thank you very muchfor your attention